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CH3F5 Bioorganic Chemistry Lecture 1 Molecular Interactions Dr Andrew Marsh, C515 [email protected] Dr Ann Dixon, C514 [email protected] Dr Rebecca Notman, G Block Room 2 [email protected] Overview Week 15 Lecture 1 Lecture 2 Introduction to molecular interactions Quantifying strength...

CH3F5 Bioorganic Chemistry Lecture 1 Molecular Interactions Dr Andrew Marsh, C515 [email protected] Dr Ann Dixon, C514 [email protected] Dr Rebecca Notman, G Block Room 2 [email protected] Overview Week 15 Lecture 1 Lecture 2 Introduction to molecular interactions Quantifying strengths of interactions Examples Class Estimation of association constant Computer Workshop 2 chymotrypsin (first was in Term 1) Week 16 Lecture 3 Lecture 4 Hydrogen bonding Aromatic interactions Computer Workshop 3 vancomycin Week 17 Lecture 5 Lecture 6 Electrostatic interactions folding Hydrophobic effect and protein folding Computer Workshop 4 beta-adrenergic receptor Week 18 Lecture 7 Lecture 8 Isothermal titration calorimetry Examples Class 2 ITC Membrane protein folding and assembly – Dr Ann Dixon Assessed Computer Workshop 5 Week 19 Lecture 9 Self-assembly and cooperativity Weeks 20/21 Revision Session Term 3 Week 30 Weds 24 Apr Assessed work deadline 2 Example: β-adrenergic receptor Adenylate cyclase, Ca2+ channels See Nature, 2009, 459, 356 and 3sn6.pdb and PDBe QUIPS summary 3 Review of Thermodynamics: Recommended reading Chemical Structure and Reactivity, J Keeler, P Wothers Chapter 6 “Thermodynamics and the Second Law” QD471.K43 Atkins’ Physical Chemistry, P W Atkins, J de Paula e.g. 8/e; Chapters 2 and 3 First Law and Second Law of Thermodynamics QD453.3.A74 Molecular Driving Forces K A Dill, S Bromberg 1/e Chapters 10, 12, 30 *** highly recommended! *** QC311.5.D55 Review of thermodynamics Consider the general reaction: A+B⇌ C+D The equilibrium constant for this reaction is given by: C ][ D ] [ Ka= [ A][ B ] May also report Kd = 1/Ka Standard state, report ΔGo and by choosing Kao = KaC0 Conventionally, C0 = 1 M and concentrations are usually expressed as M = mol dm-3 We will expect that you can all deduce the units of K for any given reaction 5 Review of thermodynamics If a mechanism involves successive reaction steps, the overall equilibrium constant is a product of the stepwise equilibrium constants (often denoted β). e.g. for the reactions: A+B⇌C+D C⇌E+F The overall K is given by: C ][ D ] [ E ][ F ] [ D ][ E ][ F ] [ K = b1 ´ b 2 = ´ = [ A][ B ] [C ] [ A][ B ] β1 β2 6 Review of thermodynamics Amount of energy capable of doing work = change in the Gibbs free energy ΔG of reaction is related to the equilibrium constant by: ΔG = –RT ln(K) Where ideal gas constant R = 8.314 J mol-1 K-1; T = temperature, Kelvin – Calculated this way, ΔG will have units of J mol-1. – Convert to kJ mol-1 by dividing by 1000. Alternatively, divide expression by (–RT) on both sides and take exponential of both sides to get: é -DG ù K = exp ê ú RT ë û 7 Review of thermodynamics The Gibbs free energy, ΔG, is energy available in a form that can be used to do work. Can be broken down into two further components: enthalpy ΔH; and entropy ΔS for a given temperature T (in Kelvin): ΔG (kcal mol-1 or kJ mol-1)= ΔH–TΔS – ΔH is heat of reaction at constant pressure (kcal mol-1 or kJ mol-1). – ΔS relates to increase/decrease in system disorder; has several components: e.g. bulk translation and rotation, configurational, etc. Caution: enthalpy and entropy are not fundamental properties of a system and decomposition of ΔG into ΔH 8 and ΔS are model dependent. Review of thermodynamics Internal energy, U(x) is associated with motions, interactions & bonding of a system. It is the fundamental property changed by e.g. ligand binding to receptor, where x is the microscopic configuration (including receptor, ligand, solvent degrees of freedom, entropy S). Potential energy V(x) is the work required to bring two molecules together to a specified distance, r. At equilibrium, the distribution of configurations within specific volume of cell or flask is given by the Boltzmann distribution: p(x) ∝ e − ((U ( x )+ pV ( x )) kBT 9 Thermodynamic quantities in biological systems In biological systems changes in pressures and molar volumes are negligible, hence enthalpy and internal energy are indistinguishable: H = (ΔU+pV) ≈ ΔU Hence although we may like to discuss entropy and enthalpy for explaining spontaneous reactions, equilibria and phase behaviour, we must be aware that they are intrinsically linked. cf. J M Fox … G M Whitesides Annu. Rev. Biophys. 2018, 10 47, 223 Molecular Interactions… Main classes of interaction (convention is —ve = more free energy) to be considered are: - electrostatic interactions ion-ion (strength ion-dipole ( dipole-dipole ( quadrupole-quadrupole ( +/- 100 - 350 kJ mol-1) +/- 50 - 200 kJ mol-1) +/- 5 - 50 kJ mol-1) +/- 5 kJ mol-1) - induction (dipole - induced dipole) - dispersion (-2.5 kJ mol-1 per atom) - repulsion (+1.5 kJ mol-1 per atom) Compare to covalent bonds e.g. C-C single bond 348 kJ mol-1 ref: Steed and Atwood Supramolecular Chemistry pp. 19-30 11 …are ingredients for the following Hydrogen bond e.g. for H2O dimer gas phase: electrostatic 118 %, induction 37 %, dispersion 42 %, repulsion –97 % π-π interactions Benzene – benzene T-shaped gas phase: electrostatic 127 %, induction 82%, dispersion & repulsion –109% Cation-π interactions K+ benzene gas phase: electrostatic 65 %, induction 47 %, dispersion & repulsion –12 % Van der Waals’ interactions argon dimer at equilibrium distance gas phase: dispersion 194 %, repulsion –94 % MP2 calculations, TR Walsh 12 Ion-ion interactions + - - effective over a long range (1/r dependence) qq - recall Coulombic interaction 1 2 - where e, e0 permittivity of medium & vacuum) 4 πεε0 r - Non-directional, high strength 100 - 350 kJ mol-1 - Many receptors for cations and anions use electrostatic interactions to hold a guest in place N Anion e.g. I- Ka [Cl-] 50 [Br-] 1020 [I-] 500 M-1 N N 5 N 13 Dipole-dipole interactions δ+ δ− O O δ− dipole magnitude = qr q is charge of each point r is distance between δ+ Dipole – dipole (brought about by inherent bond polarity) interactions have a strong orientational dependence, producing attractive or repulsive forces of the order 5 – 50 kJ mol-1 Distance dependence follows 1/r3 Often seen in solid state and evident in protein crystal structures. (For recent review see Angew. Chem. Int. Ed. Engl. 2005, 44, 1788) 55o θ µB r µA –(3cos2 θ – 1) -2 +2 +1 -1 0 x µ AµB 4πεor 3 14 Ion-dipole interactions δ+ δ− O Directional (dipole aligned for optimal binding) and strong (50 - 200 kJ mol-1) Not as long ranged as ion-ion (1/r2 dependence) + H N O O O O O NH O HN O M + O O O O O O O HN NH O O X-ray molecular structure of valinomycin - K+ complex O O N H 15 e.g. valinomycin (macrocyclic depsipeptide antibiotic isolated from Streptomyces) What is a quadrupole? Charge separation over two sites (1+ve,1-ve) gives a dipole; Charge separation over four sites (2+ve,2-ve) gives a quadrupole. For an aromatic ring, the quadrupole passes through the centre of the ring. (in very simple shape terms, it approximates to a dz2 orbital). δ- H H δ+ H H δ+ H H Represented symbolically as: δ- Θ (capital theta) is the magnitude of the quadrupole moment 16 Quadrupole-quadrupole interactions Distance dependence follows 1/r5 Strong directional dependence e.g. controls phenyl ring relative orientation H H δ- δ+ H H δ+ δ- H H H δ+ H H δ+ δ- H 55o H H δ- Represented schematically as: (end on) r +6 -3 +2 1 4 AJ Stone The Theory of Intermolecular Forces 2/e 2013, OUP + 3 4 -2 7 16 x Θ AΘB 4πεor 5 17 Induction Induction effects arise from the distortion of a molecule in the electric field of its neighbours. i.e. a permanent dipole inducing a dipole molecules approach induced dipole 18 Dispersion Sometimes referred to as van der Waals’ interactions, first quantified by London, F. (1930): induced dipole – induced dipole instantaneous dipole induced Dispersion is attractive everywhere (all distances and orientations). Is not strongly orientation dependent. Follows 1/r6 distance dependence (short-ranged) Stronger between larger and heavier atoms (QM effect) 19 Repulsion Electron-electron repulsion. Can use van der Waals’ atomic radii described by Pauling (1960) as first estimate e.g. argon dimer at equilibrium separation potential energy close approach is repulsive Computational models for repulsion take many forms. Examples are 1/r12 or exp(-r) at simple level. Rm separatuion at min. energy Rm internuclear distance Lennard-Jones potential 20 Bringing interactions together This set of archetypal interactions can be likened to a set of ingredients that when combined create a menu that we observe as molecular recognition properties of molecules. Bringing two or more molecules together results in preferences for particular orientations that can lead to particular reactivity or expressed properties. These resultant structures are highly dependent on amongst other factors: - solvent - temperature - other solutes 21 Shape and interaction complementarity These interactions between molecules are only important if they fit together correctly. This was recognised by Emil Fischer in 1894 and is called the Lock and Key Principle Although it was first use as an explanation for the specificity of enzymes for their substrates, the same ideas hold for many other stucture including designed and evolved supramolecular receptors. O H3 C O Ph NH O O OH Paclitaxel (Taxol®) potent and broad spectrum antitumour activity O Ph O H OH O OH O O CH 3 O Ph Originally derived from the bark of the Pacific Yew, T axus Br evif olia O 22 CH3F5 Lecture 2 Quantifying Molecular Interactions Dr Andrew Marsh C515 [email protected] With thanks to Professor Christopher A Hunter FRS University of Cambridge C A Hunter Angew. Chem. Int. Ed. Engl. 2004, 43, 5310 1 Free Energy Relationships Gibbs free energy, ΔG is the most useful quantity to study in order to understand intermolecular interactions. ΔG = ΔH – TΔS Free energy contributions for functional groups are additive to a first approximation. ΔGtotal = ΔGelectrostatic+ ΔGdispersion + ΔG…. How can we start to estimate free energies? 2 Interactions in Gas Phase… ΔH = ΔHelectrostatic + ΔHcharge-induced dipole + ΔHdispersion between induced dipole-induced dipoles - ΔHelectron cloud repulsion qi qj qi qj Electrostatic = c rij rij qi j i ∂+ ∂- ∂- ∂+ ∂- ∂+ Induction = c Dispersion = qi2 αj rij4 Bij rij6 Bij = c i rij αi αj √(αi/Ni) + √(αj/Nj) j Repulsion = Aij exp (- γij rij ) 3 Interactions in Gas Phase… Four terms make up overall enthalpy of interaction. ΔH = ΔHelectrostatic + ΔHcharge-induced dipole + ΔHdispersion between induced dipole-induced dipoles - ΔHelectron cloud repulsion …Into Solution The changes in the last, repulsion term can be ignored for molecules in van der Waals contact (same if complexed to solvent or another molecule) To a first approximation the effects of induced polarisation are small (e.g. 1 kJ mol-1 change in 20-25 kJ mol-1 total for urea oligomerisation – slide 10). Dispersion interactions can be estimated using the Slater-Kirkwood method… 4 Dispersion For two atoms i and j the dispersion interaction depends on atomic polarisability, αi and αj, and N, the number of valence electrons. When separated by distance r the energy can be estimated by: i j ∂- ∂+ ∂- ∂+ Dispersion = Where Bij = c Bij rij6 αi αj √(αi/Ni) + √(αj/Nj) And c is a constant. Qualitatively, larger & softer atoms (P, S, Cl…) give larger Bij values… 5 j i ∂- ∂+ Dispersion = ∂- ∂+ Slater-Kirkwood Bij values Bij = c (kJ mol-1 Å-6) Bij rij6 αi αj √(αi/Ni) + √(αj/Nj) C N O F P S Cl C 3100 2300 1800 1400 5600 5000 4200 N 2300 1700 1400 1100 4000 3600 3100 O 1800 1400 1200 900 3200 2900 2500 F 1400 1100 900 700 2400 2200 1900 P 5600 4000 3200 2400 10200 9000 7400 S 5000 3600 2900 2200 9000 8000 6700 Cl 4200 3100 2500 1900 7400 6700 5600 6 dispersion energy / surface area of contact (kJ mol-1 Å-2) C N O F P S Cl C 0.05 0.05 0.05 0.06 0.08 0.07 0.06 N 0.05 0.05 0.05 0.06 0.07 0.07 0.06 O 0.05 0.05 0.05 0.06 0.08 0.07 0.06 F 0.06 0.06 0.06 0.06 0.08 0.08 0.07 P 0.08 0.07 0.08 0.08 0.11 0.09 0.08 S 0.07 0.07 0.07 0.08 0.09 0.08 0.07 Cl 0.06 0.06 0.06 0.07 0.08 0.07 0.06 7 i j ∂- ∂+ ∂- ∂+ Dispersion = Bij rij6 8 Induction changes on complexation qi K1 ≈ 200 M-1 H2N H2N H2N K2 ≈ 800 M-1 H2N O O H2N Induction = c ∂+ ∂- qi2 αj rij4 H2N O O H2N H2N H2N H2N O H2N O H2N ∆∆G for one H-bond interaction = 20-25 kJ mol-1 ∆∆G due to polarisation = 1-2 kJ mol-1 oligomers and polymers J. Jadzyn, M. Stockhausen, B. Zywucki, J. Phys. Chem. 1987, 91, 754 A. P. Bisson, C. A. Hunter, J. C. Morales, K. Young, Chem. Eur. J. 1998, 4, 845 9 i j ∂- ∂+ ∂- ∂+ Dispersion = Bij rij6 … but because the atoms are further apart (1/r6 dependence) and in solution there are competitive interactions with solvent, the numerical value is less than expected. In fact when measured per unit surface area of contact there is little variation with atom type (effects cancel). Hence the change in dispersion energy is negligible upon complexation. 10 Electrostatics rule … These interactions can be quantified as pairwise hydrogen bonding interactions where the association constant K is found by experiment to fit a linear free energy relationship: log K = cα2Hβ2H + c1 α2H is dependent on H-bond donor properties of functional groups; β2H is dependent on H-bond acceptor properties of functional groups. c and c1 are solvent-dependent constants; c increases for decreasing solvent polarity c1 = -1.0 ± 0.1 and does not vary much with solvent. It represents the cost of complex formation in solution. 11 qi rij qj Electrostatic = c qi qj rij K D H D H A A Log K = c α2H β2H + c' 1500 experimental measurements R2 = 0.99 -1 in ∆G => +6 kJ mol c is solvent dependent cost of restricting c’ is constant -0.9 to -1.1 molecular motion [Experimentally found that for non-covalent complex formation this cost is +6 kJ mol-1 vs. +60 kJ mol-1 for a covalent interaction] M. H. Abraham, J. A. Platts, J. Org. Chem. 2001, 66, 3484 12 Calculated Molecular Electrostatic Surface Potential blue = positive (Emax) red = negative (Emin) green = neutral Me O N Me H Emax usually near an H atom Emin usually near lone pair or electron density Calculated using AM1 method and a positive point charge presented to the molecule in vacuum to calculate maximum and minimum interaction energies. 13 LFER Correlation of Emax or Emin vs. experimental H-bond properties 600 -Emin / kJ mol-1 500 400 300 Me -322 kJ mol-1 200 O N H Me 100 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 β2H Positive charge vs HB acceptor 14 250 Emax / kJ mol-1 200 150 Me 100 O -0.4 -0.2 H +146 kJ mol-1 Me 50 50 0 0.0 N 0.2 0.4 α2H 0.6 0.8 Positive charge vs HB donor 1.0 15 250 Emax / kJ mol-1 200 150 100 +84 kJ mol-1 50 -0.4 -0.2 0 0.0 0.2 0.4 α2H 0.6 0.8 1.0 Hence need to reset origin to a2H = -0.33 (measured in carbon tetrachloride) 16 600 -Emin / kJ mol-1 500 400 -33 kJ mol-1 300 200 100 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 β2H 17 Normalised α and β From line of best fit of earlier graphs, normalisation constant of 52 kJ mol-1 gives acceptor and donor values as… α = Emax / 52 kJ mol-1 = 4.1(α2H + 0.33) β = -Emin / 52 kJ mol-1 = 10.3(β2H + 0.06) 18 Change frame of reference… K D H αD βS S S H A αS βA D H A αD βA S H αS βS Log K = c α2H β2H + c' ∆G = -(αD βA + αS βS - αD βS - αS βA) + 6 kJ mol-1 ∆G = -(αD - αS) (βA - βS) + 6 kJ mol-1 ∆∆GH-bond = -(αD - αS) (βA - βS) C.A. Hunter, Angew. Chem. Int. Ed. Engl. 2004, 43, 5310 S 19 Change frame of reference… K D H αD βS S S H A αS βA D H A αD βA S H αS βS Log K = c α2H β2H + c' ∆G = -(αD βA + αS βS - αD βS - αS βA) + 6 kJ mol-1 ∆G = -(αD - αS) (βA - βS) + 6 kJ mol-1 ∆∆GH-bond = -(αD - αS) (βA - βS) Only add + 6 kJ mol-1 ONCE for the whole complex C.A. Hunter, Angew. Chem. Int. Ed. Engl. 2004, 43, 5310 S 20 … and introduce solvent A D solvent solvent D A + A A A solvent D + A D D solvent D free red = HB acceptor bound blue = HB donor Hence in any solvent, s the change in free energy ΔΔGHB … ΔΔGHB = -(αβ + αsβs) + (αβs +αsβ) ΔΔGHB = -(α-αs)(β-βs) for each interacting pair Equation A 21 F F F F Cl F F S NO O 0 1 2 N N O O 4 3 N N N 5 O 7 6 8 S O 9 P O 10 β 10 X H S H 6 H H β 0 1 8 N H R3N O H O N H OH R2 4 O O H 3 RF 2 2 O 4 α 0 4 5 6 n+ 7 H 8 CF3 F3C CF3 O H 5 Ne 22 F F F F Cl F F S NO O 0 1 2 N N O 4 3 N N N 5 O O 7 6 8 S O 9 P O 10 β N H X H 0 H 1 H S H O O H N H 2 H 3 O O H O H 4 CF3 F3C CF3 O H 5 α 23 Normalised donor / acceptor values From line of best fit of earlier graphs, normalisation constant of 52 kJ mol-1 gives acceptor and donor values as… α = Emax / 52 kJ mol-1 = 4.1(α2H + 0.33) β = -Emin / 52 kJ mol-1 = 10.3(β2H + 0.06) HB donor ability, α Alkyl ester 1.5 Amine 1.5 Chloroform 2.2 Water 2.8 Amide 2.9 Carboxylic acid 3.6 TFE 3.7 HFIP 4.5 HB acceptor ability, β Chloroform 0.8 Thiol 2.7 HFIP 3.1 Water 4.5 Ester 5.3 Alcohol 5.8 Amide 8.3 Sulfoxide 8.9 24 Interaction space α scale (donor) α > αs solute - solvent dominates solute - solute dominates solvent - solvent dominates solute - solvent dominates Blue regions HB interactions favourable leading to supramolecular complex αs α < αs β < βs βs β > βs β scale (acceptor) Note: incorrect on p. 5315 of review 25 D H αD βS S ∆∆GH-bond = -(αD - αS) (βA - βS) K S H A D H A αS βA αD βA polar α solute-solvent interactions dominate solute-solute interactions dominate solvent-solvent interactions dominate solute-solvent interactions dominate S H αS βS αS non-polar βS 0 non-polar β polar S 26 CH3F5 Lecture 3 Hydrogen Bonding Dr Andrew Marsh C515 [email protected] 1 What is a hydrogen bond? “Hydrogen bonding is a donor-acceptor interaction specifically involving hydrogen atoms” G A Jeffrey Introduction to Hydrogen Bonding, 1997 “A hydrogen bond exists between the functional group A-H, and an atom or a group of atoms, B in the same or different molecules when: (a) there is evidence of bond formation (association or chelation), (b) there is evidence that this new bond linking A-H and B specifically involves a hydrogen atom already bonded to A” Pimental and McClellan The Hydrogen Bond, 1960 δ− N δ+ H δ− δ+ O 2 Hydrogen Bond Strengths There is no such thing as a typical hydrogen bond … A-H…B interaction Strong Moderate Weak Mostly covalent Mostly electrostatic Electrostatic (gas phase) Bond lengths X-H = H-Y X-H < H-Y X-H Model Panel > Ramachandran Plot ϕ http://molprobity.biochem.duke.edu Protein folding problem Imagine 100 amino acid protein: it has 198 Φ,Ψ angles Even if each dipeptide adopts one of a few preferred conformations, the time taken for protein to randomly sample each possibility appears astronomically large (Levinthal’s paradox) But in fact certain structures and pathways are preferred and proteins fold in a more cooperative fashion. Nonetheless computational prediction of folding remains challenging …. Although application of machine learning algorithms since 2018 by Google AI DeepMind AlphaFold/2 2020 has changed this: see E Callaway Nature 2020 Cooperativity speeds up folding Protein can find its globally optimal fold without trying all possible configurations Cooperativity = probability of forming contact (e.g. C2) is much higher if another contact (e.g. C1) is already formed C1 C2 Dill et al., PNAS 1993, 90, 1942-6 Paradigm for this in proteins is the coil-helix transition Nucleation of α-helix formation – formation of 1st H-bond in helix is most difficult step, subsequent steps much easier Free energy of protein folding Proteins travel rapidly across energy landscape towards more energetically favourable conformations From Alan Fersht “Structure and Mechanism in Protein Science” Start from ensemble of unfolded states (U) and reach optimal folded state via transitions states (D and TS) What contributes to the energetics and folding pathway a protein takes? Hydrophobic effect Contributes significantly to the folding of soluble proteins Entropically-driven, often called hydrophobic collapse ΔS > 0 More hydrocarbon-water interactions: more ordered water molecules Fewer hydrocarbon-water interactions Less ordered water molecules Hydrogen Bonding & π-Interactions Contribute significantly to protein folding, especially via secondary structure formation; see Lecture 12 Enthalpically-driven (ΔH of H-bond= – (4-20) kJ mol-1) R N-terminus H N H O O H C-terminus 1 R O N H N R O N H O N N OH R H O R H O R R O H R O H R N HO H H N N N N N R O H R O H R 1O H R H O R H O R H O N N N N N N OH H O R H O R H O R O H R O H R O H R N HO R N N O H R N N O H R N O H H H Hydrogen bonds within protein Hydrogen bonds with water (hydration) Other enthalpic interactions include electrostatic, van der Waals, metal coordination, disulfide bonds Free energy of protein folding Lets look at the approx. relative contributions of these various interactions to folding: unfolded ΔG = - 50 kJ mol -1 folded ΔG = ΔH - T ΔS < 0 hydrophobic effect - TΔS > 0 +750 kJ mol -1 Protein denaturation Protein denatured by heating: TΔS contribution increases relative to contribution of Hbonds and other enthalpically favourable interactions. Exposes hydrophobic sidechains. ΔG > 0 unfolded folded ΔG = ΔH - T ΔS > 0 hydrophobic effect - T ΔS H bonds, π-interactions broken VdW electrostatic ΔG >= 0 kJ mol-1 Chain conformational entropy increased -T ΔS >>> 0 kJ mol -1 Balance shifted towards entropy – protein unfolds Human 80S ribosomal complex 4V6X.mmCIF format AM Anger et al. Nature 497, 80-85 (2013) doi:10.1038/nature12104 26 Chaperone-assisted protein folding Proteins called molecular chaperones can also help proteins fold. The two most important types of chaperones: Hsp60 – GroEL/GroES in bacteria, provide a folding chamber Hsp70 - In all living organisms, mainly prevent aggregation, especially in crowded cell Use ATP to assemble and assist Reduces energy barriers to protein folding 1aon.pdb Rasmol side view Langer, T., Pfeifer, G., Martin, J., Baumeister, W. & Hartl, F.U. Chaperonin-mediated protein folding: GroES binds to one end of the GroEL cylinder, which accommodates the protein substrate within its central cavity. EMBO J. 11, 4757–4765 (1992). Protein misfolding and disease Ab 1-42 amyloid: 2MXU F Chiti, C M Dobson Protein Misfolding, Functional Amyloid, and Human Disease Annu Rev Biochem, 2006, 75, 333 Aggregates in neurons: Parkinson’s disease Protein misfolding and disease Protein misfolds but does not form aggregates Phenylketonuria – phenyl alanine hydroxylase Protein misfolds and forms aggregates Alzheimer’s disease – amyloid (A)b-peptide Amyloidosis from haemodialysis – b2-microglobin Bovine spongiform encephalopathy Summary Hydrophobic effect is driven by entropy gained through release of associated water molecules Crucial to protein folding, assembly of cell structures Enables binding of non-polar guests in enzymes, proteins and macrocycles to give supramolecular structure KA Dill, JL MacCallum Science 2012, 338, 1042 KA Dill Protein Folding Interview CH3F5 Lecture 7 Isothermal titration calorimetry and thermodynamics Dr Andrew Marsh, C515 [email protected] Dr Ann M Dixon, C514 [email protected] Isothermal titration calorimetry Measure thermodynamic parameters of a binding process (ΔG, ΔH, ΔS) in a single experiment. Why do we want to know these values? – Free energy (ΔG) and Ka provide information on the strength of interactions (affinity) – Enthalpy (ΔH) and entropy (ΔS) reveal more about what drives complex formation and mechanism of action. conformational changes (entropy), hydrophobic effect, hydrogen bonding, aromatic interactions, dispersive interactions … Combine this information with structural data for a more detailed description of function and mechanism at a molecular level. What can we use ITC for? Popular method for studying biological and synthetic structures: – – – – – Protein-ligand interactions Enzyme inhibitors Protein-protein interactions DNA-protein interactions Molecular recognition model systems Works best in conjunction with preliminary characterization; need to know about binding sites, stoichiometry, etc. Reviews: Direct measurement of protein binding energetics by isothermal titration calorimetry, S Leavitt, E Freire Curr. Opin. Struct. Biol. 2001, 11, 560. *** Entropy-enthalpy compensation: role and ramifications in biomolecular ligand design J D Chodera, D L Mobley Annu. Rev. Biophys. 2013, 42, 121-142 Isothermal titration calorimetry Experimental setup and terms: – titrant (e.g. ligand) is titrated into the reaction cell containing the titrand, e.g. host). – The reference cell and reaction cell are maintained at the same temp. using sensors and heaters. – Measure temp. difference between sample and ref (ΔT1) and cells and jacket (ΔT2) Taken from www.microcal.com Isothermal titration calorimetry Experimental setup: – Titrant is injected in stepwise aliquots of ~1-10 μL. – For each injection, reaction between ligand and host emits/absorbs heat (exo-/endothermic) in the sample cell. – The measurement output is the power needed to keep the cells at constant temperature, as a function of time. Isothermal titration calorimetry Experimental setup: – The heat released upon binding of ligand (ΔHb) is monitored over time. – A peak is observed upon heat change, due to injection of ligand into cell. – Heat change is proportional to amount of binding: Decreases over time saturation Only heats of dilution observed – Binding curve obtained from plot of ΔH vs ligand:host molar ratio – Fit curve to determine: DHb Ka (=1/Kd), n (stoichiometry), ΔH and ΔQ (total heat of reaction) Taken from www.microcal.com Interpretation of raw data 1 Consider a 1:1 reaction stoichiometry using a multiple independent binding site model Extension to a 1:n model is possible, but won’t be considered here For a reaction between host M and ligand L: M + L ⇌ ML The heat released can be expressed as: ΔQ = V =V ΔH ΔH [Lb] [ML] Where [Lb] is concentration of bound ligand, but [Lb] is not known. Instead we need to express the heat of reaction in terms of the things we know, [Ltot] and [Mtot] Interpretation of raw data 2 é ù ê ú K [L ] tot ê ú 1 - (1+ ) /2 1 dDQ d[ML] ê1 [M tot ] 2[M tot ] ú ´ = DH ´ = DH ´ ê + 1 ú V d[Ltot ] d[Ltot ] 2 é 2 2 öù 2 æ ê ú æ [Ltot ] ö æ [Ltot ] öæ æ 1 ö 1 ö ê ú ç ÷ ê ç ÷ - 2ç ÷ç1 ÷ + ç1+ ç ÷ ÷ ú [M ] [M ] K[M ] K[M ] ê è tot øè è tot ø è tot ø ø ú êë ëè tot ø û úû In above equation we know the following for each injection: V; dΔQ/d[Ltot]; [Ltot]; [Mtot] Using a non-linear least squares analysis, we use the above equation and experimental data to obtain fitted values for ΔH, K, and (where applicable) n. The best fit of these three parameters will best represent the sigmoidal curve (i.e. cumulative integrated heat vs. concentration) Interpretation of raw data 3 Errors in measurements and problems in how data is fitted to frequently lead to uncertainty that is greater than values obtained. See: Bayesian analysis of isothermal titration calorimetry for binding thermodynamics T. H. Nguyen … J Chodera PLoS ONE 2018, 13, e0203224 There are two open source methods I am aware of that are applicable to the analysis of primary ITC data, both written in python: Bayesian ITC https://github.com/choderalab/bayesian-itc PyTC https://github.com/harmslab/pytc Limitations on the conditions Ligand and host will need to be in the same buffer and salt conditions concentration) Viable temperature range is roughly 5-60 C ‘Wiseman factor’ c = K [Mtot]; works for c = 10 – 1000 Effective Ka upper limit 108 – 109 M-1 Taken from Leavitt and Freire, Current Opinion in Structural Biology 2001, 11, 560–566 For original work see: T Wiseman, S Williston, JF Brandts, L-N Nin Anal. Biochem. 1989, 179, 131-137 Review of thermodynamics The heat capacity at constant pressure of a system, Cp, is given by: DH Cp = T So the change in heat capacity for a reaction carried out over a range of temperatures is given by: DH 2 - DH1 DC p = T2 - T1 Hence plot graph of ΔH vs T to check linearity & obtain gradient, ΔCp 11 Heat capacity data Measuring ΔHapp over a range of temperatures allows an estimate of ΔCp Large negative change in ΔCp, suggests change in surface hydration in the free vs complexed systems. In other words, when ΔCp < 0, interpreted as water being removed from the solute surface and returned to the bulk solvent. However! May also indicate protein structural reorganisation. Experimental analyses justify this claim; see analysis of H2O vs D2O solvation Chervenak and Toone, JACS, 1994, 116, 10533 Nozaki and Tanford J Biol Chem 1971, 246, 2211-2217 Challenges/pitfalls of ITC measurement/interpretation Requires relatively large quantities of protein and ligand Weak association constant makes this worse Remember to measure and account for self-association Coupled and complex equilibria require more sophisticated algorithms, see methods such as: by Chodera Lab https://github.com/choderalab/bayesian-itc and Harms Lab https://github.com/harmslab/pytc Example 1: Statin binding to HMG-CoA reductase Statins inhibit the enzyme HMG-CoA reductase that is the key step in the biosynthesis of cholesterol in the body. They share a common motif, but differ in their hydrophobic part O O OH O OH O OH O OH O O O OH OH OH O O O O O OH F O N Me HO pravastatin compactin hydroxyacid simvastatin hydroxyacid fluvastatin polyketide synthase metabolites O O OH O OH OH O O OH O OH OH F F F O O N N N HN N S O Carbonell and Freire, Biochemistry 2005, 44, 11741 cerivastatin atorvastatin O rosuvastatin Binding of: compactin (A), simvastatin (B), fluvastatin (C), cerivastatin (D), atorvastatin (E), and rosuvastatin (F) to human HMGR. Interactions between the HMG moieties of the statins and the protein are mostly ionic or polar. E. S. Istvan, J. Deisenhofer Science 2001, 292,1160-1164 Example 1: Statins Data (at 25 C) demonstrates entropically-driven binding (i.e. entropy large and positive) ΔCp indicates that this entropy change is due to solvent reorganization X-ray crystallography of statin-enzyme complexes indicate the enzyme conformation doesn’t change upon binding Statin ΔH (kcal mol-1) ΔG (kcal mol-1) TΔS (kcal mol-1) ΔCp (cal mol1 K-1) pravastatin -2.5 -9.7 7.2 -0.14 cerivastatin -3.3 -11.4 8.1 -0.15 atorvastatin -4.3 -10.9 6.6 -0.17 rosuvastatin -9.3 -12.3 3.0 -0.46 Example 2: renin inhibitors Renin is an aspartyl protease upstream of the potent vasoconstrictor angiotensin II and inhibitors have potential as therapeutics to reduce high blood pressure. F O F O N O N O NH O O H N S H 2N N H H 2N N N N N NH2 N N NH2 NH2 Inhibitor 1 7IG in 2iko.pdb renin IC50 6500 nM R W Sarver et al. Analytical Biochemistry, 2007, 360, 30-40 LIY in 2iku.pdb 58 nM LIX in 2il2.pdb 27 nM ITC data for inhibitors vs. renin in buffer at 301 K 5 HB Fewer waters More than one binding mode inhibitor 1 3 11 Ka M-1 0.28 x 106 12.6 x 106 12.7 x 106 DG° kcalM-1 –7.50 –9.77 –9.78 DH° kcalM-1 –9.50 –10.00 –9.35 TDS° kcalM-1 –2.00 –0.23 0.43 n 1 1 1 Systems with large c values For a Wiseman factor c = K [Mtot] > 1000 use a competition binding experiment described by B W Sigurskold Analytical Biochemistry 2000, 277, 260-266; see also J Chem Educ 2015, 92, 1552-1556. Example: HIV-1 protease with inhibitor KN-764 ITC profile shows Wiseman c is too large ITC binding with both inhibitors present allows measurement of improved binding profile Arch. of Biochem. Biophys. 2001, 390, 169-175 O O O H N N H O O N H N OH OH NH O S HIV-1 protease with KNI-764 1 msn.pdb H N N H O HIV-1 protease with Ac pepstatin 5hvp.pdb OH N H OH O OH O Using a mixture of ligands, gives a better titration curve K(apparent) = 3.1 x 1010 M-1 (wild type HIV-1 protease) O O NH O N H N OH S OH [KNI-764] = 250 uM O O O H N N H H N N H O OH N H OH O OH O [Ac pepstatin] = 200 uM A Velazquez-Campoy, Y Kiso, E Freire Arch. of Biochem. Biophys. 2001, 390, 169-175 Apparent change in enthalpy Change in enthalpy measured for a system is not necessarily a direct measure of the interactions between the molecules in a complex Should refer to ΔH as “apparent” change in enthalpy (ΔHapp) Example: a ligand may bind to a host, but in the process the conformation of the host changes, e.g.: ΔHapp = ΔHb + ΔHconf The structural change ΔHconf may be deduced from the X-ray molecular structures and molecular simulation Apparent change in enthalpy Another common contribution to ΔHapp may be proton transfer when the host and ligand bind This will not always be obvious – need to run experiments at the same pH but using different buffers. The buffer should differ in ionization enthalpy. Change in ΔHapp with buffer is a strong sign of proton transfer ΔHapp = ΔHb + (nH+) ΔHbuffer Tables of buffer ionization enthalpies are available in the literature. Summary Contrast the enthalpy-driven binding of the renin inhibitors with the entropy-driven binding of the statin-HMG CoA reductase system ITC allows researchers to link ΔG back to structural information There are other effects to be taken into account, e.g.: salt effects: if the binding affinities change substantially with salt concentration, suspect electrostatic interactions between host and ligand size effects: if an inclusion complex is formed, how “snug” is the fit? More room for the bound ligand to move means more configurational entropy. ITC is almost always complemented by other characterization methods Summary 2 You should now be able to: Calculate thermodynamic properties given typical output from an ITC experiment Interpret ITC data taking into account conformational changes, protonation processes, salt concentration, solven reorganization, etc Explain how systems with very large binding affinities may be successfully measured using ITC (competition assay) Read and evaluate papers in the scientific literature So lets try some examples ….. ! CH3F5 Membrane protein folding and assembly Dr. Ann Dixon | [email protected] Outline of key concepts Chemistry of amino acids Introduction to membrane proteins Differences in amino acid sequences in soluble and membrane proteins. Structure prediction Hydrophobicity scales Two-stage model of membrane protein folding The role of the membrane Proteins Control majority of biological functions Made up of amino acids: – 20 naturallyoccurring amino acids – each has different structural/chemical properties Proteins Two general families of proteins: – Water-soluble (aqueous) – Membrane (not water soluble) Soluble proteins found in aqueous environment of cells Membrane proteins associated with cell membranes http://heme-coag.uthscsa.edu/ Cell Membranes Made up of phospholipids arranged to form a bilayer Cell Membranes Define boundary of the cell & organelles Contain a variety of lipid types which impart characteristic properties Marinko, J.T. et al. Chem. Rev. 2019, 119, 5537−5606 Membrane Proteins Account for ~30% of the proteins encoded in human genome Perform critical functions in cell Transport of molecules / ions Signals across membranes Cell adhesion Viral infection Structural stability Moreau, C. J. et al. Coupling ion channels to receptors for biomolecule sensing. Nature Nanotechnology 3, 620-625 (2008) Hydrophobic effect Familiar with hydrophobic effect – – – – hydrophobic regions cluster together in aqueous environment energetically favourable drives folding of soluble proteins in solution (review?) drives association of membrane proteins with membrane bilayers Integral Peripheral Reproduced from pbil.ibcp.fr/.../membrane_interaction1.html Membrane protein sequence To promote association with membrane, amino acid sequence in membrane proteins is different than in soluble proteins: – Six hydrophobic amino acids (L, I, V, A, F, G) ~ 65% of all membrane-associated regions. – Very few polar / charged residues. Q P WC H DE K R N L Y M L I O H3C OH H3C CH3 NH2 A OH NH2 F O H3 C OH NH2 T CH3 O H3C G O OH NH2 V CH3 O OH NH2 O H2 N I S V G OH F A Senes et al, J. Mol. Biol. (2000) 296, 921. Transmembrane domains Soluble Membrane Integral membrane proteins span the bilayer one time or many times Contains membrane-spanning regions (transmembrane [TM] domains) – 20-25 hydrophobic amino acids, usually flanked by Trp or Tyr – Separated by stretches of hydrophilic amino acids (loops) – Topology encoded by charge at the boundaries “+ve inside (i.e. cytoplasm) rule” TM domains can weave across membrane bilayer Structure prediction Given an AA sequence, can use chemical properties of amino acids to predict location of TM domains using hydrophobicity scales – E.g. Wimley-White chemical hydrophobicity scales: One of the first scales reported Describes energetics of protein : bilayer interactions Experimentally-determined transfer free energies of each amino acid – To create scales: Measured partitioning of peptides between water and: – Synthetic POPC bilayer interface – n-octanol – Non-polar amino acids favoured in bilayer – Large energy cost for dragging polar residues into membrane Can predict partitioning into bilayer. – Interface scale: partitioning of protein to water:bilayer interface – Octanol scale: partitioning of folded protein into the bilayer interior. Interface Scale 2.5 E 1.5 D K R H 0.5 -0.5 Q P N HA T SV G charged arom MC I L -1.5 Y F W -2.5 Wimley and White, Nat. Struct. Biol., 1996, 10, 842-848. DG (water-to-octanol, kcal mol-1) Energetics: what does it tell us about relative energies of insertion? DG (water-to-bilayer, kcal mol-1) Wimley-White hydrophobicity scales Octanol Scale 4 E D 3 2 K R H 0 -1 -2 -3 N Q 1 P G A S H T C arom charged V M I L Y F W Wimley, Creamer, and White, Biochemistry, 1996, 35, 5109-5124. Many (inter)faces of a membrane Gurtovenko et al. (2008) J. Phys. Chem. 112:4629-4634-9302. Early methods: Hydropathy plots Using hydrophobicity scales, can predict location of TM domains with a hydropathy plot. – Eg. MerF membrane protein sequence: Mercury transporter in gram10 20 30 40 50 60 70 80 MKDPKTLLRV SIIGTTLVAL CCFTPVLVIL LGVVGLSALT GYLDYVLLPA LAIFIGLTIY AIQRKRQADA CCTPKFNGVK K – Enter sequence into hydropathy plot calculation software (eg Membrane Protein Explorer or MPEx) – Plot output – TM domains appear as positive peaks Hydropathy (kcal/mol) 8 3 -2 1 11 21 31 41 51 -7 -12 -17 TMD 1 TMD 2 Residue Number 61 71 81 Hydropathy plots Using hydrophobicity scales, can predict location of TM domains with a hydropathy plot. – Eg. MerF membrane protein sequence: Mercury transporter in gram10 20 30 40 50 60 70 80 MKDPKTLLRV SIIGTTLVAL CCFTPVLVIL LGVVGLSALT GYLDYVLLPA LAIFIGLTIY AIQRKRQADA CCTPKFNGVK K TMD1 (12-36) TMD2 (45-62) Lu GJ, Tian Y, Vora N, Marassi FM, Opella SJ (2013) J. Am. Chem. Soc. 135(25):9299-9302. Biological hydrophobicity scale Measures insertion of hydrophobic sequences into cell membrane and stability of protein in the membrane 4 – Chemical thermodynamics can explain complex cellular processes such as membrane insertion. 3.5 3 DGapp (kcal mol-1) Correlates well with Wimley-White chemical scale 2.5 2 1.5 1 0.5 0 -0.5 -1 I L F V C M A W T Y G S N H P Q R E K D Amino acid Hessa et al, Nature, 2005, 433, p. 377-381 Topology prediction with TOPCONS (consensus) Tsirigos, K,D. et al., Nucl Acids Res, 2015, W401-W407. Chow, M., et al., Prot. Expr. Purif., 2018, 152, 31-39. Topology prediction with TMHMM Based on a hidden Markov model (HMM) approach Makes it possible to model hydrophobicity, charge bias, helix lengths, and grammatical constraints into one model Eg. MerF membrane protein: TMD1 (13-35) and TMD2 (45-62) Krogh, A. et al., J. Mol. Biol., 2001, 567-580. Topology prediction with DeepTMHMM Utilises all known proteomes to improve prediction – best performing method so far Eg. MerF membrane protein: TMD1 (11-31) TMD2 (43-63) https://dtu.biolib.com/DeepTMHMM Membrane protein primary structure So far, thermodynamics can explain the primary structure (e.g. sequence) of membrane proteins: – Problem: Hydrophobicity scales show that thermodynamic cost of placing polar amino acids into membrane is high. – Solution: Bulk of amino acid side chains in TM domain are non-polar. Now try Activity 1 Membrane protein secondary structure Thermodynamics also explains secondary structure of membrane proteins: – Problem: C=O and NH groups along protein backbone are also very polar. – Solution: All participate in hydrogen bonds - accomplished by formation of a-helices and b-sheets. – lowers cost of insertion into membrane. a-helix b-sheet Membrane protein tertiary structure Two general structural classes: a-helical bundle b-sheet / b-barrel e.g. Bacteriorhodopsin e.g. PagP T. Kouyama, T. Nishikawa, T. Tokuhisa, H. Okumura, J.Mol.Biol. 335 pp. 531 (2004) V. E. Ahn, E. I. Lo, C. K. Engel, L. Chen, P. M. Hwang, L. E. Kay, R. E. Bishop, G. G. Prive, EMBO J. 23 pp. 2931 (2004) Folding.... Membrane protein folding Two Stage Model: TM helix-helix interactions drive folding and assembly of membrane proteins and complexes Membrane protein folding in 2 thermodynamically distinct stages Stage I: Hydrophobic sequences form stable transbilayer a-helices Popot, J.L and Engelman, D.M. (1990) Biochemistry 29:4031-4037. Stage II: Lateral association of transbilayer a-helices Prediction of folding In soluble proteins, folding initiated by hydrophobic effect – Shield hydrophobic regions from aqueous solution Membrane proteins already in hydrophobic environment – Hydrophobic effect less important – In membrane, folding primarily driven by: hydrogen bonding electrostatic interactions close packing side chains Interactions are stronger, energetically more favourable in non-polar environment. Association motifs Stabilise strong & specific interactions between TM domains GXXXG motif Glycophorin A Polar-residue mediated Amino-acid Permease GAPI Leucine-zipper MHC Class II Invariant Chain Q Q Q Schneider et al, 2004 FEBS Letts, 577, 5-8. Dawson et al, 2002, J. Mol. Biol., 316, p.799 Dixon et al., 2006 Biochemistry, 45, p.5228 http://chemistry.umeche.maine.edu All employ a network of non-covalent interactions to stabilise interaction. – Multiple weak interactions have cumulative effect. Helical wheels Predict possible interactions with the membrane using a two-dimensional plot of sequence: helical wheels – 2D projection down the centre of the helix. – Plot sequence of a-helical membrane spanning domains on a helical wheel. – Search for known interaction motifs on the same "face" of the a-helix. – E.g. for the linear sequence: AVLLMFIGLLAG – the helical wheel looks like... Helical wheel tools online http://heliquest.ipmc.cnrs.fr Heliquest http://heliquest.ipmc.cnrs.fr Role of the membrane on protein fold The membrane environment impacts fold of membrane proteins Gurtovenko et al. (2008) J. Phys. Chem. 112:4629-4634-9302. Depth dependence Certain amino acids can only stably inhabit certain regions (depths) of the membrane. – Leu, Ala, Val, Ile and Phe most stable at centre of bilayer, most hydrophobic environment – His, Tyr, and Trp most stable at the more polar “edges”, where the acly chains meet the polar headgroups – Arg, Asp, Glu and Lys most stable outside the bilayer, accessing the polar aqueous surrounding Ulmschneider, M. B.; Sansom, M. S.; Di Nola, A. Proteins: Struct., Funct., Genet. 2005, 59, 252−265. Protein Tilt Transmembrane domains adapt to bilayer thickness. – Thinning of the membrane causes TM domains to tilt – Alternatively, bilayer may be locally distorted to accommodate a long TMD. – Thickening of bilayer may lead to extension of a TM helix out of the bilayer Tilting of the TM domain can affect the fold of the protein. Marinko, J.T. et al. Chem. Rev. 2019, 119, 5537−5606 Peripheral membrane proteins So far, have focussed mainly on integral membrane proteins. Other important classes of membrane protein. Integral Peripheral Reproduced from pbil.ibcp.fr/.../membrane_interaction1.html E.g. Antimicrobial peptides Duplantier and van Hoek, Front. Immunol., 2013, http://dx.doi.org/10.3389/fimmu.2013.00143 Amphipathic a-helices Present in membrane-associated proteins Have hydrophobic and hydrophilic "faces" of the helix – Helix lays on surface of membrane, with hydrophilic face exposed to solution. membrane bilayer Hydrophilic face Hydrophobic face Hydrophilic face Hydrophobic face Find amphipathic a-helix using a helical wheel Plot the sequence of the membrane-associated CAP18 protein and find the hydrophobic face GLRKRLRKFRNKIKEKLKKIGQKIQGLP e b a f d g c Find amphipathic a-helix using a helical wheel Plot the sequence of the membrane-associated CAP18 protein and find the hydrophobic face GLRKRLRKFRNKIKEKLKKIGQKIQGLLP – hydrophobic – hydrophilic – unique R,K,K,G L,F,K,K e G,K,E,Q,R b a f K,N,K,Q L,I,I,L d g R,K,G,L c R,R,L,I Hydrophobic moment measures amphipathic-ness Cap18 APH GpA TM Summary Membrane proteins have different "rules" for sequence and folding. Using chemical thermodynamics, we can begin to understand these proteins. Have developed tools to predict location of TM domains and mechanisms of folding – Hydrophobicity scales – Hydropathy plots – Helical wheels Crystal structure of oxygen-evolving photosystem II at a resolution of 1.9 Å, Yasufumi Umena, Keisuke Kawakami, Jian-Ren Shen & Nobuo Kamiya, Nature, 473, 55–60, 2011, doi:10.1038/nature09913 Now try Activities 2 and 3 If you like any of this please talk to me about MChem projects! CH3F5 Lecture 9 Physicochemical methods: measuring self-assembly and cooperativity Dr Andrew Marsh C515 [email protected] 1 Today’s Lecture 1. Methods to determine association constants and stoichiometry 2. Data analysis 3. Self-assembled structures 4. Cooperativity 2 Overview – what do we need to know? Molecular and supramolecular structure in solid state and solution Molecular weight of aggregate(s) or protein complex(es) Association constant(s) Structural e.g. X-ray diffraction, NMR, Electron Microscopy in ‘solid’ state Need methods in solution, gel phase; good data analysis and computational tools e.g. MD to link them all together. Useful references: 1. Principles and Methods in Supramolecular Chemistry H-J Schneider, A Yatsimirsky Wiley, 2001. QD381.S35 2. Biophysics in Drug Discovery: impact, challenges and opportunities J-P Renaud et al. Nature Rev. Drug Discovery 2016, 15, 69 3. Comprehensive Supramolecular Chemistry, Pergamon, 1996 4. Binding Constants K A Connors, Wiley 1987 3 Methods to determine Ka and stoichiometry Isothermal Titration Calorimetry (ITC) Solution NMR spectroscopy – complexation induced shifts (CIS); titration for Ka – intermolecular nOe measurements – diffusion measurements (r), DOSY UV, fluorescence inc. thermal unfolding and thermophoresis of fluorophore labels Surface Plasmon Resonance or Quartz Crystal Microbalance methods (interface) Vapour pressure osmometry – Mn determination Consider ‘throughput’ of technique …. 4 Methods for Ka determination Method Medium logKa Conc 10x M Quantity 1H Any -3 0.1-2 mg UV-vis H2O best f(e) -2 to -4 10-100 µg Fluor. H2O best 2-7 -3 to -6 1-10 µg Calorimetry Many Range -1 to -3 1-10 mg Chromat. Mainly H2O 2-5? -2 to -6 0.1 to 1 µg SPR/QCM Many 3-15 - Immob. ligand NMR H-J Schneider and A Yatsimirsky, 2001 J-P Renaud Nature Rev. Drug Discovery 2016, 15, 69 K Hirose in ‘Analytical Methods in Supramolecular Chemistry’ 2012, 27-66 5 Choice of method & concentration e.g if [Guest] = 10-5 M 100 log K = 5 80% %complex present log K= 4 50 20% 0 -5 -4 -3 -2 -1 log [host] work between 20-80% complexation for greatest accuracy; self-association must also be quantified 6 NMR – Complexation Induced Shifts CIS in ppm 0.00 +0.90 +0.15 +1.25 -0.45 N N SO3 -0.10 N N +0.10 OH +1.70 +1.00 follow by titration... HO +1.50 7 NMR Titration maximum gives stoichiometry Job’s plot (may!) give stoichiometry, but see: D B Hibbert, P Thordarson Chem Commun, 2016, 52, 12792 [complex] And use OpenDataFit 0 0.5 [host] 1 [host]+[guest] 10 Dd ppm Titrate and follow shift of one or more signals 9 10 9 10 9 increase conc. ppm [guest] **Excellent review** : Pall Thordarson, Chem Soc Rev 2011, 40, 1305 8 Data analysis x x x x x x x 1/Δδ Δδ ppm x x slope = 1/(KΔδinfinity) x Δδinfinity x x xx x x x x [guest] least squares curve fitting see CH271 Module. 1/[guest] -Ka Benesi-Hildebrand plot OpenDataFit for 1:1, 1:2 and 2:1 equilibria http://opendatafit.org; self-association. Global fit of multiple equilibria is possible but non-trivial! (cf. ITC for example, BayesianITC and PyTC approaches). Reviews: D B Hibbert, P Thordarson Chem Commun, 2016, 52, 12792 K Hirose in ‘Quantitative Analytical Supramolecular Chemistry’ 2012, 27-66 9 UV-visible or fluorescence Spectroscopy Titrate one component into another change as function of concentration Number of isosbestic points usually corresponds to number of microstates (β1, β2 …βn) present. Abs Least squares fit can be used to extract association constants wavelength, nm 10 Vapour pressure osmometry - Mn Depends on the colligative properties of a solution (Raoult’s law or Henry’s law for non-ideal solutions) Vapour pressure above a solution depends on the number of particles in solution, so a molecule of known molecular weight m which aggregates in solution will give an apparent molecular weight n × m Hence aggregation number n can be calculated by calibration against a standard Practicalities: Measured using difference in resistance between two thermistors with a drop of solution on one and pure solvent on another via a Wheatstone bridge (interfaced to a computer and analysis software to make it easier …) 11 Henry’s Law and van ’t Hoff factor, i Osmotic pressure, vapour pressure and other colligative properties depend on number of particles in solution. The van ’t Hoff factor, i is the ratio between the actual concentration of particles when a compound or mixture is dissolved and the concentration calculated from its molecular mass. a Is the fraction of n moles of solute which associate in a solvent: 1 i = 1 (1 ) n Hence i 1 if dissociation takes place) For example acetic acid dimerises (n=2): Hence if α = 1 i.e. all molecules associate); i = ½ 1 i = 1 (1 ) 2 i =1 2 12 Examples OC10H21 O O H C10H21O O H O H O O H O OC10H21 O D O H O O O H H O O O C10H21O O H O O H O H O D O H N N O N H A N O A H N A D H O OC10H21 H N H MW by VPO shows hexamer (CHCl3) Chem Commun 1996, 1527. O TIPSO OTIP S O O O H OC10H21 N N TIPSO TIPSO MW by VPO = 4600 – 4900 (12-35 mM) vs. calc. 4531 A D Hamilton et al. Tetrahedron Letters, 1994, 35, 3665. N O 7 H N N N N H H N O H N N H H H N O N N N H O N N OTIP S OTIP S H O O 2 TIPSO OTIP S MW by VPO = 1841 vs. calc 2285 Org. Biomol. Chem. 2009, 2093-2103. 13 Self-assembly Is the principle by which a complex structure may be built up, often in a cooperative (“all-or-nothing”) fashion from smaller components. In a biological context, advantages over conventional, covalent assembly: 1. Use of only a few repeating subunits reduces the amount of genetic information required. 2. Association through multiple weak interactions allows for assembly / disassembly, hence error correcting. 3. A large structure can be constructed with greater efficiency. 14 What is meant by cooperativity? “The whole has an effect greater than the sum of the parts”. TWO types of cooperativity can be observed: allosteric cooperativity seen in oxygen binding to the haemoglobin tetramer; classically described by Hill equation chelate cooperativity difference in strength between inter- and intramolecular interactions due to effective molarity; classic biological examples protein or DNA folding. Definitive review with mathematical description of both, including statistical factors: C A Hunter, H L Anderson ACIEE 2009, 48, 7488-7499 Allosteric cooperativity: haemoglobin Haemoglobin tetramer 1A3N.pdb Oxygen binding curves of myoglobin (muscle) and haemoglobin (blood) - Haemoglobin (tetramer) sigmoidal, myoglobin (monomeric) greater affinity at a given pO2 Reference system: one site, monovalent ligand B K A B Receptor A 𝐴 𝐵 =𝐾 𝐴 𝐵 Receptor 𝐴 ! = 𝐴 + 𝐴 𝐵 = 𝐴 1+𝐾 𝐵 𝐵 ! = 𝐵 + 𝐴 𝐵 𝐵 𝐴 𝐵 𝐾𝐵 = 𝐴! 1+𝐾 𝐵 𝐴 1 = 𝐴 ! 1+𝐾 𝐵 𝐴 𝐵 𝐾𝐵 𝜃" = = 𝐴! 1+𝐾 𝐵 C A Hunter, H L Anderson ACIEE 2009, 48, 7488-7499 17 = 0 ! [ A] 0 1 + K[ B] Reference system: ligand binding [ A B] K[ B] " A "= = [ A B] = = K[ B] K[ B] A [ A] 0 [ A 1B] +1=K[ B] " [=A] + K[ B] A ! [0A] 0 1 + K[ B] WeWe useuse Log(K[B] thethenormalized on the thex-axis x-axisofofthe thebinding binding isotherms, so that po 0) 0as Log(K[B] ) as normalizedconcentration concentration scale scale on isotherms, so that the the point We use Log(K[B] 0) as the normalized concentration scale on the x-axis of the binding isotherms, so that the point at w bound occurs at zero onon thethex-axis, throughthe theorigin. origin. bound occurs at zero x-axis,and andthe theHill Hillplot plot passes passes through ! bound occurs at zero on the x-axis, and the Hill plot passes through the origin. (a) (a) (a) (b) (b)(b) θA θA θA (c) (c) (c) θθAA LogcRcR==2.0 2.0 Log Log cR = 2.0 Log Log θAθ /(1)θA)θA) Log θθAA/(1A/(110 10 θθAA ===10 A 11 11 11 θA = 11 θA = 111 Log K [B]0 θA =11 11 K [B]0 K [B]0 Log K [B]0 Log K [B]0 Log K [B]0 Log K [B]0 K [B]0 Log K [B]0 Figure S.1. a) The binding isotherm for titration of a monovalent ligand B into a single-site receptor A, at constant [A]0, where Figure a) The binding isotherm for0 titration a monovalent ligand B into receptorscale A, atillustrates constantmeasure [A]0, wh TheS.1. receptor is 50% bound when [B] = 1/K. b)of The binding isotherm plotted onaasingle-site Log concentration Figure S.1. a) The binding isotherm for titration of a monovalent ligand B into a single-site receptor A, at constant [A] The concentration receptor is 50% boundwindow, when [B] b) The binding isotherm plotted on a Log switching Log for this system. c) The corresponding Hill concentration plot. The slope scale at the illustrates origin is themeas Hill0 0 =c1/K. R = 2.0 Theconcentration receptor is this 50% boundwindow, when [B] b)for The binding isotherm plotted on a Log concentration 0 = = 1.0 for system. switching Log c R1/K. = 2.0 this system. c) The corresponding Hill plot. The slope scale at the illustrates origin is them Hill plot concentration switching = 1.0 for this system. window, Log c R = 2.0 for this system. c) The corresponding Hill plot. The slope at the origin is = 1.0 for this system. Dilution experiments. The reference experiment for oligomerization of AB is dilution of an equimolar mixture of A a total concentrations are equal ([A]0 = [B] can be calculated on [B]ofasan follows: 0), speciation Dilution experiments. The reference experiment forprofiles oligomerization of AB based is dilution equimolar mixture of total concentrations areB] equal ([A] profiles can be calculated on [B]ofasan follows: Dilution experiments. The for oligomerization of ABbased is dilution equimolar mixture 0), speciation [ A B]= K[ A][ = K[reference B] 20 = [B]experiment 18 total concentrations are equal ([A] 2 0 = [B]0), speciation profiles can be calculated based on [B] as follows: [ A B]= K[ A][ B] = K[ B] C A Hunter, H L Anderson ACIEE 2009, 48, 7488-7499 [ A] = [ A] +[ A B] = [ B](1 + K[ B]) Allosteric ligand binding B B 2K1 B 1 2 + + K2 AA AA B2 AA B 𝐴𝐴 𝐵 = 2𝐾# 𝐴𝐴 𝐵 𝐴𝐴 𝐵 ! ! K= K1K2 𝐴𝐴 𝐵$ = 𝐾#𝐾$ $ 𝐴𝐴 𝐵 = 𝐴𝐴 + 𝐴𝐴 𝐵 + 𝐴𝐴 𝐵$ = 𝐴𝐴 *1 + 2𝐾# 𝐵 + 𝐾#𝐾$ 𝐵 = 𝐵 + 𝐴𝐴 𝐵 + 𝐴𝐴 ≈ 𝐵 C A Hunter, H L Anderson ACIEE 2009, 48, 7488-7499 19 $ 𝐴𝐴 1 = 𝐴𝐴 ! 1 + 2𝐾# 𝐵 + 𝐾#𝐾$ 𝐵 𝐴𝐴 𝐵 2𝐾# 𝐵 = 𝐴𝐴 ! 1 + 2𝐾# 𝐵 + 𝐾#𝐾$ 𝐵 𝐴𝐴 𝐵$ 𝐾#𝐾$ 𝐵 $ = 𝐴𝐴 ! 1 + 2𝐾# 𝐵 + 𝐾#𝐾$ 𝐵 Proportion bound is 𝜃" And define: 𝐾% = $ $ $ 1 𝐴𝐴 𝐵 + 𝐴𝐴 𝐵$ 𝐾𝐵 2 𝜃" = = 𝐴𝐴 ! 1+𝐾 𝐵 𝐾#𝐾$ and an interaction, molecular parameter (cooperativity measure) 𝛼 = 20 !! !" [AA] 0 Allosteric ligand binding, We use Log(K’[B] ) as the x-axis of the speciation profiles, where K’ = √K K , so that the point at which A is 50 speciation zero on the x-axis, and the Hill plot passes through the origin, forcurves any value of α (where α = K /K ). 1 + 2K1[ B] + K1K 2[ B] 0 1 2 2 (a) (b) population Log K' [B]0 1 (c) population population Log K' [B]0 Log K' [B]0 a = 0.01 a=1 a =100 positive cooperativity no cooperativity negative cooperativity (red, intermediates; blue, assembled Make initial binding events less favourable (a)% (b) (c) 𝐾 𝐾#𝐾$ and later θbinding events more favourable θ= Figure S.4. Speciation profiles for titration of a monovalent ligand B into a two-site receptor AA, where [B]0 >> [AA]0: fully blue, intermediate AA B in red, and total binding site occupancy θA in black. The speciation profile for the corresponding r with one binding site is also shown (grey dots). a) positive cooperativity, α = 100. b) no cooperativity, α = 1. c) negative co 0.01. In a), the population of AA B2 and θA are practically identical. The x-axis is calculated using K’ = √K1K2, except for th reference system where K’ = K (grey dots). A A Log cR = 1.1 Log cR = 2.0 Log cR = 3.9 Log θA/(1-θA) θA = 10 11 C A Hunter, H L Anderson ACIEE 2009, 48, 7488-7499 0.5 21 Binding calculated binding isotherm for N = 4 with modera isotherm of O2 (“B”) binding to constants). Hb (“A”) θA K' [B]0 Circles = experimental data, black line = calculated, Figure S.9. The binding isotherm for oxygen (B) binding grey line = single site A B reference system all Ki+1 = αKi (black). The binding isotherm for the A B sy axis is calculated using2009, K’ = 1/[B]. C A Hunter, H L Anderson ACIEE 48, 507488-7499 Chelate cooperativity BB AA n K 4K 1 2 oligomers K EM AA (BB)2 𝐸𝑀 = 𝜎 &("#$$ &&) &($$ &( ) where 𝜎 = 2 is a statistical factor accounting for difference in binding site concentration for a monovalent ligand (B) and divalent ligand (B…B) C A Hunter, H L Anderson ACIEE 2009, 48, 7488-7499 solution is twice that in the B solution. We therefore use Log(K’[BB]0) as the x-axis of the speciation profiles, where K’ = 2√K1K in systems where the closed macrocyclic complex c-AA BB is not populated, the1point at which AA is 50% bound occurs at z 2 x-axis. No allosteric cooperativity, a =1, i.e. K = K in all cases (a) (b) population 2[BB]0 = 1 K2EM (c) population population 2[BB]0 = EM Log K' [BB]0 Log K' [BB]0 Log K' [BB]0 Figure S.15. Speciation profiles for titration of a divalent ligand BB into a two-site receptor AA, where [BB]0 >> [AA]0: cyclic comple AA BB in green, open intermediate o-AA BB in red, 2:1 complex AA (BB)2 in blue, and total binding site occupancy, θA, in black. Th speciation profile for the A B system with one intermolecular interaction is shown for reference (grey dots). a) K EM = 100. b) K EM EM = 0.01. The x-axis is calculated using K’ = 2K, and in all cases, α = 1, i.e. K1 = K2 = K. K EM = 100 red, intermediates; blue, assembled green, cyclic K EM = 1 K EM = 0.01 C A Hunter, H L Anderson ACIEE 2009, 48, 7488-7499 24 “Rosette” Structure O H N (H3C)3C C(CH3)3 N N H O N O H H H N N N N N N (H3C)3C C(CH3)3 H H O N N H H N N N O H H N H H O N O N O H H H N N N H O N H N C(CH3)3 N C(CH3)3 Zerkowski, J.A.; Seto, C.T.; Whitesides, G.M. J. Am. Chem. Soc. 1992, 5473 25 Cooperativity in self-assembled rosette R R N H N O N R N R H O 3x H N N O H O R R H N R N N H H R N O H H N N R H O N N N N H N H O O R R N N H N N R H H H R N O R N O O N N N N N H H H 3x H N H H N H H N O N H R R Effective molarity, EM ≈ 2 M K EM = 100 – 10,000 M-1 P Motloch C A Hunter Org. Biomol. Chem. 2020, 18, 1602 26 Diffusion ordered (DOSY) NMR Einstein-Smoluchowski equation 𝐷 = !! " # combined with Stokes’ law 𝑓 = 6𝜋𝜂𝑟$ for either a spherical, ellipsoidal or disc-like object moving at random through chloroform (viscosity h = 0.563 10-3 Pa⋅s at T = 293 K) to give: Sphere Prolate sphere (ellipsoid) Oblate sphere (disc) l rs 𝑘/ 𝑇 𝐷= 6𝜋𝜂𝑟0 l h h k BT D= h2 6 tan 1 k BT D= l2 h2 l2 l2 h2 6 tan 1 l2 h2 l2 l2 E. L. Cussler, Diffusion: Mass Transfer in Fluid Systems, 3/e CUP, 2009 Review: Y Cohen, L Avram, T Evan-Salem, S Slovak, N Shemesh, L Frish in 27 ‘Analytical Methods in Supramolecular Chemistry’ 2012, 197-285. Example: single, double and triple cyanurate melamine rosette, all modelled as sphere Mw D cm2 s-1 rs Å 1723 4235 7899 0.55 ± 0.01 0.34 ± 0.01 0.27 ± 0.01 7.3 ± 0.2 11.8 ± 0.4 14.9 ± 0.5 28 P Timmerman … L Frish, Y Cohen J. Chem. Soc. Perkin Trans., 2000, 2, 2077–2089 intensity Gel permeation chromatography retention time DETECT (UV, RI...) 29 Example: rosette structures Comparison of the stability of rosette aggregates assayed by gel permeation chromatography. HB = no. of hydrogen bonds, N = no. of particles in aggregate (JACS, 1996, 118, 12614) G M Whitesides et al. Acc. Chem. Res. 1995, 28, 37 O H N (H3C)3C C(CH3)3 N N H N N H N N H H H O N O N O O N O H H H H H H N N N N N N N N N (H3C)3C C(CH3)3 H H O H N O H N H O N H N C(CH3)3 N C(CH3)3 Zerkowski, J.A.; Seto, C.T.; Whitesides, G.M. J. Am. Chem. Soc. 1992, 5473 30 Summary X-ray diffraction excellent structural technique NMR gives structural and thermodynamic data ITC can access thermodynamic data Self-association (dimer, oligomer …) in solution needs to be quantified Need more than one technique for a true picture! Self-assembly is central to biological systems Allosteric cooperativity can be positive or negative; example is oxygen binding to haemoglobin Chelate cooperativity arises from effective molarity (EM) in intramolecular systems being higher than intermolecular 31